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Number Theory

Source: Poland - Second Round 2020 P5

February 8, 2020
number theoryprime numbers

Problem Statement

Let p>p> be a prime number and SS be a set of p+1p+1 integers. Prove that there exist pairwise distinct numbers a1,a2,...,ap−1∈Sa_1,a_2,...,a_{p-1}\in S that a1+2a2+3a3+...+(p−1)ap−1 a_1+2a_2+3a_3+...+(p-1)a_{p-1} is divisible by pp.
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